SOLUTION: find the vertex, the line of symmetry and the maximum or minimum value of f(x). Graph the function f(x)=1/2(x+6)^2+3

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Question 236217: find the vertex, the line of symmetry and the maximum or minimum value of f(x). Graph the function f(x)=1/2(x+6)^2+3
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
find the vertex, the line of symmetry and the maximum or minimum value of f(x). Graph the function f(x)=1/2(x+6)^2+3
------------------
Vertex (-6,3)
Line of symmetry: x = -6
Minimum at the vertex is f(x)=3
-----------------------

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Cheers,
Stan H.

Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!


The equation

is
a parabola with a vertex at (h,k) and which passes
through the points (h+1,k+a) and (h-1,k+a), and its
axis of symmetry is the vertical line whose equation
is
So in the problem:

, ,
[Notice that the sign is changed for h but kept for k]
So the vertex is (h,k) or (-6,3),
The parabola passes through (h-1,k+a) and (h+1,k+a), or
(-6-1,3+) or (-7,) and
(-6+1,3+) or (-5,)
Its axis of symmetry is the vertical line whose equation
is or
We plot the vertex (-6,3)

We draw the axis of symmetry which is a vertical line
through the vertex (the green line below:

Then we plot the two points,
one on each side of the vertex
(-7,) and (-5,)



Finally we sketch in the parabola:

Edwin
 

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